Further studies upon the problem of freedom are to be found in Boutroux’s lectures given at the Sorbonne in 1892-93 in the course entitled _De l’Idée de la Loi naturelle dans la Science et la Philosophie contemporaines_. He there recognises in freedom the crucial question at issue between the scientists and the philosophers, for he states the object of this course of lectures as being a critical examination of the notion we have of the laws of nature, with a view to determining the situation of human personality, particularly in regard to free action.[21] Boutroux recognises that when the domain of science was less extensive and less rigorous than it is now it was much easier to believe in freedom. The belief in Destiny possessed by the ancients has faded, but we may well ask ourselves, says Boutroux, whether modern science has not replaced it by a yet more rigorous fatalism.[22] He considers that the modern doctrine of determinism rests upon two assumptions—namely, that mathematics is a perfectly intelligible science, and is the expression of absolute determinism; also that mathematics can be applied with exactness to reality. These assumptions the lecturer shows to be unjustifiable. Mathematics and experience can never be fitted exactly into each other, for there are elements in our experience and in our own nature which cannot be mathematically expressed. This Boutroux well emphasises in his lecture upon sociological laws, where he asserts that history cannot be regarded as the unrolling of a single law, nor can the principle of causality, strictly speaking, be applied to it.[23] An antecedent certainly may be an influence but not a cause, as properly understood. He here agrees with Renouvier s position and attitude to history, and shows the vital bearing of the problem of freedom upon the philosophy of history, to which we shall presently give our special attention. [21] _De l’Idée de la Loi naturelle_, Lecture IV., p. 29. [22] Compare Janet’s remark, given on p. 136. [23] Lecture XIII. Instead of the ideal of science, a mathematical unity, experience shows us, Boutroux affirms, a hierarchy of beings, displaying variety and spontaneity—in short, freedom. So far, therefore, from modern science being an advocate of universal determinism, it is really, when rightly regarded, a demonstration, not of necessity, but of freedom. Boutroux’s treatment of the problem of freedom thus demonstrates very clearly its connection with that of science, and also with that of progress. It forms pre-eminently the central problem.